How many triangles can you make on the 3 by 3 pegboard?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
This activity investigates how you might make squares and pentominoes from Polydron.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?
These practical challenges are all about making a 'tray' and covering it with paper.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
What do these two triangles have in common? How are they related?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
What is the largest number of circles we can fit into the frame
without them overlapping? How do you know? What will happen if you
try the other shapes?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you put these shapes in order of size? Start with the smallest.
How many models can you find which obey these rules?
How many different cuboids can you make when you use four CDs or
DVDs? How about using five, then six?
This practical investigation invites you to make tessellating
shapes in a similar way to the artist Escher.
What shapes can you make by folding an A4 piece of paper?
Explore the triangles that can be made with seven sticks of the
This practical activity involves measuring length/distance.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
What happens to the area of a square if you double the length of
the sides? Try the same thing with rectangles, diamonds and other
shapes. How do the four smaller ones fit into the larger one?
Can you make the most extraordinary, the most amazing, the most
unusual patterns/designs from these triangles which are made in a
Using a loop of string stretched around three of your fingers, what
different triangles can you make? Draw them and sort them into
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
An activity making various patterns with 2 x 1 rectangular tiles.
Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Can you visualise what shape this piece of paper will make when it is folded?
Here is a version of the game 'Happy Families' for you to make and
Have you noticed that triangles are used in manmade structures?
Perhaps there is a good reason for this? 'Test a Triangle' and see
how rigid triangles are.
Can you see which tile is the odd one out in this design? Using the
basic tile, can you make a repeating pattern to decorate our wall?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Can you make the birds from the egg tangram?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
Galileo, a famous inventor who lived about 400 years ago, came up
with an idea similar to this for making a time measuring
instrument. Can you turn your pendulum into an accurate minute
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?